Gaussian rational

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In mathematics, the field of Gaussian rationals is the field Q(i) formed by adjoining the imaginary number i to the field of rationals. It therefore provides an example of an algebraic number field. It consists of the complex numbers of the form p + qi, where p and q are both rational, and is an example of a quadratic field.

The field of Gaussian rationals is neither ordered nor topologically complete. The Gaussian integers Z[i] form the ring of integers of Q(i).


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